Compute $\sqrt{2^2\cdot 3^4}$.
Rewriting $2^2\cdot 3^4$ as $(2\cdot3^2)^2$ shows us that $\sqrt{2^2\cdot 3^4}=\sqrt{(2\cdot3^2)^2}=2\cdot3^2=2\cdot9=\boxed{18}$.